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General Relativity and Quantum Cosmology, gr-qc
Abstract:
Understanding the Bondi-Metzner-Sachs (BMS) frame of the gravitational waves
produced by numerical relativity is crucial for ensuring that analyses on such
waveforms are performed properly. It is also important that models are built
from waveforms in the same BMS frame. Up until now, however, the BMS frame of
numerical waveforms has not been thoroughly examined, largely because the
necessary tools have not existed. In this paper, we show how to analyze and map
to a suitable BMS frame for numerical waveforms calculated with the Spectral
Einstein Code (SpEC). However, the methods and tools that we present are
general and can be applied to any numerical waveforms. We present an extensive
study of 13 binary black hole systems that broadly span parameter space. From
these simulations, we extract the strain and also the Weyl scalars using both
SpECTRE's Cauchy-characteristic extraction module and also the standard
extrapolation procedure with a displacement memory correction applied during
post-processing. First, we show that the current center-of-mass correction used
to map these waveforms to the center-of-mass frame is not as effective as
previously thought. Consequently, we also develop an improved correction that
utilizes asymptotic Poincar\'e charges instead of a Newtonian center-of-mass
trajectory. Next, we map our waveforms to the post-Newtonian (PN) BMS frame
using a PN strain waveform. This helps us find the unique BMS transformation
that minimizes the $L^{2}$ norm of the difference between the numerical and PN
strain waveforms during the early inspiral phase. We find that once the
waveforms are mapped to the PN BMS frame, they can be hybridized with a PN
strain waveform much more effectively than if one used any of the previous
alignment schemes, which only utilize the Poincar\'e transformations.
